Generation and manipulation of isotropic droplets in nematic medium using switchable dielectrophoresis

Dielectrophoresis (DEP) in a medium with anisotropic dielectric susceptibility is very different from typical DEP in an isotropic medium: The direction of particle actuation can be switched depending on the direction of the susceptibility tensor of the medium. However, the understanding of switchable DEP (SDEP) in an anisotropic medium is still in its infant stage. Here, we investigate SDEP using heat-generated isotropic droplets in a nematic liquid crystal (LC) medium. We demonstrate that the location of the generation of isotropic droplets can be partially controlled by controlling the temperature gradient within the LC cell using dielectric loss. The SDEP actuation of isotropic droplets is also highly dependent on the location of the isotropic droplets. Using this method, we fabricated different array patterns of isotropic and nematic phase separations under different applied signals.

Figure 1

(a) Perpendicular (${\varepsilon }_{\perp }$) and parallel (${\varepsilon }_{\parallel }$) dielectric constant at 60 Hz, (b) elastic constants, and (c) rotational viscosity of MLC-7026-000 as a function of temperature.

Figure 2

(a) The LC cell configuration. The width of electrodes and their interspace are 10 and 50 $\mu \mathrm{m}$, respectively. (b) Equipotential lines and LC director distribution at the cross section of the cell under the application of a 10-V, 60-Hz square-wave signal. (c) Tensor coefficient F and permittivity difference tensor ($\mathrm{\Delta }{\mathit{\varepsilon }}_{IN}$) between ${\mathit{\varepsilon }}_I$ and ${\mathit{\varepsilon }}_N$. (d) Schematics for the variation of ${\mathbf{F}}_{\mathrm{SDEP}}$ direction depending on the LC director.

Figure 3

(a) The cross-sectional views of the LC director profile along the electrode (black line) and (b) along the diagonal direction (purple line) at 15, 30, and 50 V, respectively. The LC director distribution along the electrode dramatically changes depending on the applied voltages [see the black squares in (a)], but the variation of the LC director along the diagonal direction is small, as shown in (b).

Figure 4

(a) The top view, and (b) the cross-sectional views of normalized E (that is, $\mathbf{E}/{\mathbf{E}}_{\max }$) fields along the electrode [black line at (a)], and (c) along the diagonal direction [purple diagonal line at (a)] at 15, 30, and 50 V, respectively. The normalized E is not changed significantly. ${\mathbf{E}}_{\max }$ is 1.6, 3.3, and 5.5 V/μm, at 15, 30, and 50 V, respectively.

Figure 5

(a) The top view, and (b) the cross-sectional views of the normalized $\mathbf{\nabla }{\mathbf{E}}^2$ (that is, $\mathbf{\nabla }{\mathbf{E}}^2/\mathbf{\nabla }{\mathbf{E}}_{max}^2$) along the electrode [black line at (a)], and (c) along the diagonal direction [purple diagonal line at (a)] at 15, 30, and 50 V, respectively. The normalized magnitude of $\mathbf{\nabla }{\mathbf{E}}^2$, that is, $\mathbf{\nabla }{\mathbf{E}}^2/\mathbf{\nabla }{\mathbf{E}}_{max}^2$, is expressed by the background color. $\mathbf{\nabla }{\mathbf{E}}_{max}^2$ is approximately $9\times {10}^{17}$, $3\times {10}^{18}$, and $1\times {10}^{19}{\mathrm{V}}^2/{\mathrm{m}}^3$, at 15, 30, and 50 V, respectively.

Figure 6

(a–c) Procedure of generation, migration, and growth of isotropic droplets at 15 V. (a) Isotropic droplets are randomly generated near $T_{NI}$. (b) Yellow dotted line indicates the migration of the droplets by ${\mathbf{F}}_{\mathrm{SDEP}}$. (c) After 58 s, the isotropic droplets are located either on the middle of the electrode (${\mathrm{A}}_1$ type) or around M (${\mathrm{B}}_1$ type). (d) LC director profile. (e) $\mathbf{\nabla }{\mathbf{E}}^2$ profile. (f) ${\mathbf{F}}_{\mathrm{SDEP}}$ vector fields (arrows) and $\mathrm{\Delta }{U}_{\mathrm{total}}$ profile (background color). (g) ${\mathbf{F}}_{\mathrm{SDEP}}$ vector field profile (arrows) and the magnitude of ${\mathbf{F}}_{\mathrm{SDEP}}$ (background color). Scale bars, 20 $\mu \mathrm{m}$.

Figure 7

(a–c) Procedure of generation, migration, and growth of isotropic droplets at 30 V. Scale bars, 20 $\mu \mathrm{m}$. (a–b) The generation of isotropic droplets near H (the white circle) and their radial migration. (c) Diagonally aligned droplets after stopping the migration (see Supplemental Video S2 [38]). (d) LC director profile, (e) ${\mathbf{F}}_{\mathrm{SDEP}}$ vector fields (arrows), $\mathrm{\Delta }{U}_{\mathrm{total}}$ profile (background color), and (f) the magnitude of ${\mathbf{F}}_{\mathrm{SDEP}}$ (background color). (g) Isotropic droplet migration trajectories (yellow dotted and white solid lines).

Figure 8

(a) Generation and migration of isotropic droplets at 50 V. (b) ${\mathbf{E}}^2$ profile across the H point, representing the relative scale of dielectric loss. (c) Droplet generation controlled by switching the frequency between 30 and 40 kHz. (d) Generation and migration of isotropic droplets at 15-V signal with the frequency of 60 Hz or 100 kHz.

Figure 9

(a) Periodic array of ${\mathrm{A}}_3$-type isotropic droplets located at the L points after stopping the droplet migration (see Supplemental Video S3 [38]). (b) $\mathrm{\Delta }{U}_{\mathrm{total}}$ profile near the H area. The left and right panels have log scale and linear scale vertical axes, respectively. (c) ${\mathbf{F}}_{\mathrm{SDEP}}$ (arrows) and $\mathrm{\Delta }{U}_{\mathrm{total}}$ profiles (background color) at 50 V. (d) LC director profile.

Figure 10

(a) When the isotropic droplet grows, it is deformed, squeezed, and escapes from L to M. The yellow dotted lines represent the direction of ${\mathbf{F}}_{\mathrm{MDEP}}$, and the black solid lines represent the moving direction of the droplet. (b) Contour lines of the magnitude of ${\mathbf{F}}_{\mathrm{SDEP}}$ around the square-shaped droplet [white box in the first image of (a)] and (c) the elliptical-shaped droplet [white box in the last image of (a)].